Differentiate the following w.r.t.x
(i)` (2)/((3x +1)` (ii) `(3x +5)/(4x +6)`

Answer

(i) `(-6)/((3x +1)^2)` (ii) `(-2)/((4x +6)^2)`

Explanation

(i) `(dy)/(dx) = ((3x+1)(d)/(dx)(2) - 2(d)/(dx)(3x+1))/((3x+1)^2) =((3x+1)xx0-2(3+0))/((3x+1)^(2))=(-6)/((3x+1)^(2))`
`(ii)(dy)/(dx)=((4x+6)d/(dx)(3x+5)-(3x+5)d/(dx)(4x+6))/((4x+6)^(2))=((4+6)(3+0)-(3x+5)(4+0))/((4x+6)^2)`
`=(12x +18 - 12x - 20)/((4x+6)^2) = (-2)/((4x+6)^2)`